Foundations of Physics

, Volume 49, Issue 11, pp 1287–1305 | Cite as

The Cosmological Constant From Planckian Fluctuations and the Averaging Procedure

  • S. ViaggiuEmail author


In this paper I continue the investigation in Viaggiu (Class Quantum Gravity 35:215011, 2018), Viaggiu (Phys Scr 94:125014, 2019) concerning my proposal on the nature of the cosmological constant. In particular, I study both mathematically and physically the quantum Planckian context and I provide, in order to depict quantum fluctuations and in absence of a complete quantum gravity theory, a semiclassical solution where an effective inhomogeneous metric at Planckian scales or above is averaged. In such a framework, a generalization of the well known Buchert formalism (Buchert in Gen Relativ Gravit 33:1381, 2001) is obtained with the foliation in terms of the mean value \(s({\hat{t}})\) of the time operator \({\hat{t}}\) in a maximally localizing state \(\{s\}\) of a quantum spacetime (Doplicher et al. in Commun Math Phys 172:187, 1995; Doplicher in Space-time and fields: a quantum texture, in Karpacz, new developments in fundamental interaction theories, arXiv:hep-th/0105251, 2001; Bahns et al. in Advances in algebraic quantum field theory, Springer, Cham; Tomassini and Viaggiu in Class Quantum Gravity 28:075001, 2011) and in a cosmological context (Tomassini and Viaggiu in Class Quantum Gravity 31:185001, 2014). As a result, after introducing a decoherence length scale \(L_D\) where quantum fluctuations are averaged on, a classical de Sitter universe emerges with a small cosmological constant depending on \(L_D\) and frozen in a true vacuum state (lowest energy), provided that the kinematical backreaction is negligible at that scale \(L_D\). Finally, I analyse the case with a non-vanishing initial spatial curvature \({\mathcal {R}}\) showing that, for a reasonable large class of models, spatial curvature and kinematical backreation \({\mathcal {Q}}\) are suppressed by the dynamical evolution of the spacetime.


Cosmological constant Planckian fluctuations Misner-Sharp energy Averaging procedure 



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Authors and Affiliations

  1. 1.Dipartimento di Fisica Nucleare, Subnucleare e delle RadiazioniUniversitá degli Studi Guglielmo MarconiRomeItaly
  2. 2.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly
  3. 3.INFN, Sezione di Napoli, Complesso Universitario di Monte S. AngeloNapoliItaly

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